Dimensionality Reduction with a LargeVislike method
Description
Carry out dimensionality reduction of a dataset using a method similar to
LargeVis (Tang et al., 2016).
Usage
lvish(
X,
perplexity = 50,
n_neighbors = perplexity * 3,
n_components = 2,
metric = "euclidean",
n_epochs = 1,
learning_rate = 1,
scale = "maxabs",
init = "lvrandom",
init_sdev = NULL,
repulsion_strength = 7,
negative_sample_rate = 5,
nn_method = NULL,
n_trees = 50,
search_k = 2 * n_neighbors * n_trees,
n_threads = NULL,
n_sgd_threads = 0,
grain_size = 1,
kernel = "gauss",
pca = NULL,
pca_center = TRUE,
pcg_rand = TRUE,
fast_sgd = FALSE,
ret_nn = FALSE,
ret_extra = c(),
tmpdir = tempdir(),
verbose = getOption("verbose", TRUE),
batch = FALSE,
opt_args = NULL,
epoch_callback = NULL,
pca_method = NULL,
binary_edge_weights = FALSE,
nn_args = list()
)
Arguments
X 
Input data. Can be a data.frame , matrix ,
dist object or sparseMatrix .
Matrix and data frames should contain one observation per row. Data frames
will have any nonnumeric columns removed, although factor columns will be
used if explicitly included via metric (see the help for
metric for details). A sparse matrix is interpreted as a distance
matrix, and is assumed to be symmetric, so you can also pass in an
explicitly upper or lower triangular sparse matrix to save storage. There
must be at least n_neighbors nonzero distances for each row. Both
implicit and explicit zero entries are ignored. Set zero distances you want
to keep to an arbitrarily small nonzero value (e.g. 1e10 ).
X can also be NULL if precomputed nearest neighbor data is
passed to nn_method , and init is not "spca" or
"pca" .

perplexity 
Controls the size of the local neighborhood used for
manifold approximation. This is the analogous to n_neighbors in
umap . Change this, rather than n_neighbors .

n_neighbors 
The number of neighbors to use when calculating the
perplexity . Usually set to three times the value of the
perplexity . Must be at least as large as perplexity .

n_components 
The dimension of the space to embed into. This defaults
to 2 to provide easy visualization, but can reasonably be set to any
integer value in the range 2 to 100 .

metric 
Type of distance metric to use to find nearest neighbors. For
nn_method = "annoy" this can be one of:

"euclidean" (the default)

"cosine"

"manhattan"

"hamming"

"correlation" (a distance based on the Pearson correlation)

"categorical" (see below)
For nn_method = "hnsw" this can be one of:

"euclidean"

"cosine"

"correlation"
If rnndescent is
installed and nn_method = "nndescent" is specified then many more
metrics are avaiable, including:

"braycurtis"

"canberra"

"chebyshev"

"dice"

"hamming"

"hellinger"

"jaccard"

"jensenshannon"

"kulsinski"

"rogerstanimoto"

"russellrao"

"sokalmichener"

"sokalsneath"

"spearmanr"

"symmetrickl"

"tsss"

"yule"
For more details see the package documentation of rnndescent .
For nn_method = "fnn" , the distance metric is always "euclidean".
If X is a data frame or matrix, then multiple metrics can be
specified, by passing a list to this argument, where the name of each item in
the list is one of the metric names above. The value of each list item should
be a vector giving the names or integer ids of the columns to be included in
a calculation, e.g. metric = list(euclidean = 1:4, manhattan = 5:10) .
Each metric calculation results in a separate fuzzy simplicial set, which are
intersected together to produce the final set. Metric names can be repeated.
Because nonnumeric columns are removed from the data frame, it is safer to
use column names than integer ids.
Factor columns can also be used by specifying the metric name
"categorical" . Factor columns are treated different from numeric
columns and although multiple factor columns can be specified in a vector,
each factor column specified is processed individually. If you specify
a nonfactor column, it will be coerced to a factor.
For a given data block, you may override the pca and pca_center
arguments for that block, by providing a list with one unnamed item
containing the column names or ids, and then any of the pca or
pca_center overrides as named items, e.g. metric =
list(euclidean = 1:4, manhattan = list(5:10, pca_center = FALSE)) . This
exists to allow mixed binary and realvalued data to be included and to have
PCA applied to both, but with centering applied only to the realvalued data
(it is typical not to apply centering to binary data before PCA is applied).

n_epochs 
Number of epochs to use during the optimization of the
embedded coordinates. The default is calculate the number of epochs
dynamically based on dataset size, to give the same number of edge samples
as the LargeVis defaults. This is usually substantially larger than the
UMAP defaults. If n_epochs = 0 , then coordinates determined by
"init" will be returned.

learning_rate 
Initial learning rate used in optimization of the
coordinates.

scale 
Scaling to apply to X if it is a data frame or matrix:
"none" or FALSE or NULL No scaling.
"Z" or "scale" or TRUE Scale each column to
zero mean and variance 1.
"maxabs" Center each column to mean 0, then divide each
element by the maximum absolute value over the entire matrix.
"range" Range scale the entire matrix, so the smallest
element is 0 and the largest is 1.
"colrange" Scale each column in the range (0,1).
For lvish, the default is "maxabs" , for consistency with LargeVis.

init 
Type of initialization for the coordinates. Options are:

"spectral" Spectral embedding using the normalized Laplacian
of the fuzzy 1skeleton, with Gaussian noise added.

"normlaplacian" . Spectral embedding using the normalized
Laplacian of the fuzzy 1skeleton, without noise.

"random" . Coordinates assigned using a uniform random
distribution between 10 and 10.

"lvrandom" . Coordinates assigned using a Gaussian
distribution with standard deviation 1e4, as used in LargeVis
(Tang et al., 2016) and tSNE.

"laplacian" . Spectral embedding using the Laplacian Eigenmap
(Belkin and Niyogi, 2002).

"pca" . The first two principal components from PCA of
X if X is a data frame, and from a 2dimensional classical
MDS if X is of class "dist" .

"spca" . Like "pca" , but each dimension is then scaled
so the standard deviation is 1e4, to give a distribution similar to that
used in tSNE and LargeVis. This is an alias for init = "pca",
init_sdev = 1e4 .

"agspectral" An "approximate global" modification of
"spectral" which all edges in the graph to a value of 1, and then
sets a random number of edges (negative_sample_rate edges per
vertex) to 0.1, to approximate the effect of nonlocal affinities.
A matrix of initial coordinates.
For spectral initializations, ("spectral" , "normlaplacian" ,
"laplacian" , "agspectral" ), if more than one connected
component is identified, no spectral initialization is attempted. Instead
a PCAbased initialization is attempted. If verbose = TRUE the
number of connected components are logged to the console. The existence of
multiple connected components implies that a global view of the data cannot
be attained with this initialization. Increasing the value of
n_neighbors may help.

init_sdev 
If nonNULL , scales each dimension of the initialized
coordinates (including any usersupplied matrix) to this standard
deviation. By default no scaling is carried out, except when init =
"spca" , in which case the value is 0.0001 . Scaling the input may
help if the unscaled versions result in initial coordinates with large
interpoint distances or outliers. This usually results in small gradients
during optimization and very little progress being made to the layout.
Shrinking the initial embedding by rescaling can help under these
circumstances. Scaling the result of init = "pca" is usually
recommended and init = "spca" as an alias for init = "pca",
init_sdev = 1e4 but for the spectral initializations the scaled versions
usually aren't necessary unless you are using a large value of
n_neighbors (e.g. n_neighbors = 150 or higher). For
compatibility with recent versions of the Python UMAP package, if you are
using init = "spectral" , then you should also set
init_sdev = "range" , which will range scale each of the columns
containing the initial data between 010. This is not set by default to
maintain backwards compatibility with previous versions of uwot.

repulsion_strength 
Weighting applied to negative samples in low
dimensional embedding optimization. Values higher than one will result in
greater weight being given to negative samples.

negative_sample_rate 
The number of negative edge/1simplex samples to
use per positive edge/1simplex sample in optimizing the low dimensional
embedding.

nn_method 
Method for finding nearest neighbors. Options are:

"fnn" . Use exact nearest neighbors via the
FNN package.

"annoy" Use approximate nearest neighbors via the
RcppAnnoy package.

"hnsw" Use approximate nearest neighbors with the
Hierarchical Navigable Small World (HNSW) method (Malkov and Yashunin,
2018) via the
RcppHNSW package.
RcppHNSW is not a dependency of this package: this option is
only available if you have installed RcppHNSW yourself. Also,
HNSW only supports the following arguments for metric :
"euclidean" , "cosine" and "correlation" .

"nndescent" Use approximate nearest neighbors with the
Nearest Neighbor Descent method (Dong et al., 2011) via the
rnndescent
package. rnndescent is not a dependency of this package: this
option is only available if you have installed rnndescent
yourself.
By default, if X has less than 4,096 vertices, the exact nearest
neighbors are found. Otherwise, approximate nearest neighbors are used.
You may also pass precalculated nearest neighbor data to this argument. It
must be a list consisting of two elements:

"idx" . A n_vertices x n_neighbors matrix
containing the integer indexes of the nearest neighbors in X . Each
vertex is considered to be its own nearest neighbor, i.e.
idx[, 1] == 1:n_vertices .

"dist" . A n_vertices x n_neighbors matrix
containing the distances of the nearest neighbors.
Multiple nearest neighbor data (e.g. from two different precomputed
metrics) can be passed by passing a list containing the nearest neighbor
data lists as items.
The n_neighbors parameter is ignored when using precomputed
nearest neighbor data.

n_trees 
Number of trees to build when constructing the nearest
neighbor index. The more trees specified, the larger the index, but the
better the results. With search_k , determines the accuracy of the
Annoy nearest neighbor search. Only used if the nn_method is
"annoy" . Sensible values are between 10 to 100 .

search_k 
Number of nodes to search during the neighbor retrieval. The
larger k, the more the accurate results, but the longer the search takes.
With n_trees , determines the accuracy of the Annoy nearest neighbor
search. Only used if the nn_method is "annoy" .

n_threads 
Number of threads to use (except during stochastic gradient
descent). Default is half the number of concurrent threads supported by the
system. For nearest neighbor search, only applies if
nn_method = "annoy" . If n_threads > 1 , then the Annoy index
will be temporarily written to disk in the location determined by
tempfile .

n_sgd_threads 
Number of threads to use during stochastic gradient
descent. If set to > 1, then be aware that if batch = FALSE , results
will not be reproducible, even if set.seed is called with a
fixed seed before running. Set to "auto" to use the same value as
n_threads .

grain_size 
The minimum amount of work to do on each thread. If this
value is set high enough, then less than n_threads or
n_sgd_threads will be used for processing, which might give a
performance improvement if the overhead of thread management and context
switching was outweighing the improvement due to concurrent processing.
This should be left at default (1 ) and work will be spread evenly
over all the threads specified.

kernel 
Type of kernel function to create input probabilities. Can be
one of "gauss" (the default) or "knn" . "gauss" uses
the usual Gaussian weighted similarities. "knn" assigns equal
probabilities to every edge in the nearest neighbor graph, and zero
otherwise, using perplexity nearest neighbors. The n_neighbors
parameter is ignored in this case.

pca 
If set to a positive integer value, reduce data to this number of
columns using PCA. Doesn't applied if the distance metric is
"hamming" , or the dimensions of the data is larger than the
number specified (i.e. number of rows and columns must be larger than the
value of this parameter). If you have > 100 columns in a data frame or
matrix, reducing the number of columns in this way may substantially
increase the performance of the nearest neighbor search at the cost of a
potential decrease in accuracy. In many tSNE applications, a value of 50
is recommended, although there's no guarantee that this is appropriate for
all settings.

pca_center 
If TRUE , center the columns of X before
carrying out PCA. For binary data, it's recommended to set this to
FALSE .

pcg_rand 
If TRUE , use the PCG random number generator (O'Neill,
2014) during optimization. Otherwise, use the faster (but probably less
statistically good) Tausworthe "taus88" generator. The default is
TRUE .

fast_sgd 
If TRUE , then the following combination of parameters
is set: pcg_rand = TRUE and n_sgd_threads = "auto" . The
default is FALSE . Setting this to TRUE will speed up the
stochastic optimization phase, but give a potentially less accurate
embedding, and which will not be exactly reproducible even with a fixed
seed. For visualization, fast_sgd = TRUE will give perfectly good
results. For more generic dimensionality reduction, it's safer to leave
fast_sgd = FALSE . If fast_sgd = TRUE , then usersupplied
values of pcg_rand and n_sgd_threads , are ignored.

ret_nn 
If TRUE , then in addition to the embedding, also return
nearest neighbor data that can be used as input to nn_method to
avoid the overhead of repeatedly calculating the nearest neighbors when
manipulating unrelated parameters (e.g. min_dist , n_epochs ,
init ). See the "Value" section for the names of the list items. If
FALSE , just return the coordinates. Note that the nearest neighbors
could be sensitive to data scaling, so be wary of reusing nearest neighbor
data if modifying the scale parameter.


A vector indicating what extra data to return. May contain
any combination of the following strings:

"nn" same as setting ret_nn = TRUE .

"P" the high dimensional probability matrix. The graph
is returned as a sparse symmetric N x N matrix of class
dgCMatrixclass, where a nonzero entry (i, j) gives the
input probability (or similarity or affinity) of the edge connecting
vertex i and vertex j. Note that the graph is further sparsified by
removing edges with sufficiently low membership strength that they
would not be sampled by the probabilistic edge sampling employed for
optimization and therefore the number of nonzero elements in the
matrix is dependent on n_epochs . If you are only interested in
the fuzzy input graph (e.g. for clustering), setting
n_epochs = 0 will avoid any further sparsifying. Be aware that
setting binary_edge_weights = TRUE will affect this graph (all
nonzero edge weights will be 1).

sigma a vector of the bandwidths used to calibrate the input
Gaussians to reproduce the target "perplexity" .

tmpdir 
Temporary directory to store nearest neighbor indexes during
nearest neighbor search. Default is tempdir . The index is
only written to disk if n_threads > 1 and
nn_method = "annoy" ; otherwise, this parameter is ignored.

verbose 
If TRUE , log details to the console.

batch 
If TRUE , then embedding coordinates are updated at the
end of each epoch rather than during the epoch. In batch mode, results are
reproducible with a fixed random seed even with n_sgd_threads > 1 ,
at the cost of a slightly higher memory use. You may also have to modify
learning_rate and increase n_epochs , so whether this provides
a speed increase over the singlethreaded optimization is likely to be
dataset and hardwaredependent.

opt_args 
A list of optimizer parameters, used when
batch = TRUE . The default optimization method used is Adam (Kingma
and Ba, 2014).

method The optimization method to use. Either "adam"
or "sgd" (stochastic gradient descent). Default: "adam" .

beta1 (Adam only). The weighting parameter for the
exponential moving average of the first moment estimator. Effectively the
momentum parameter. Should be a floating point value between 0 and 1.
Higher values can smooth oscillatory updates in poorlyconditioned
situations and may allow for a larger learning_rate to be
specified, but too high can cause divergence. Default: 0.5 .

beta2 (Adam only). The weighting parameter for the
exponential moving average of the uncentered second moment estimator.
Should be a floating point value between 0 and 1. Controls the degree of
adaptivity in the stepsize. Higher values put more weight on previous
time steps. Default: 0.9 .

eps (Adam only). Intended to be a small value to prevent
division by zero, but in practice can also affect convergence due to its
interaction with beta2 . Higher values reduce the effect of the
stepsize adaptivity and bring the behavior closer to stochastic gradient
descent with momentum. Typical values are between 1e8 and 1e3. Default:
1e7 .

alpha The initial learning rate. Default: the value of the
learning_rate parameter.

epoch_callback 
A function which will be invoked at the end of every
epoch. Its signature should be: (epoch, n_epochs, coords) , where:

epoch The current epoch number (between 1 and
n_epochs ).

n_epochs Number of epochs to use during the optimization of
the embedded coordinates.

coords The embedded coordinates as of the end of the current
epoch, as a matrix with dimensions (N, n_components ).

pca_method 
Method to carry out any PCA dimensionality reduction when
the pca parameter is specified. Allowed values are:
"irlba" . Uses prcomp_irlba from the
irlba package.
"rsvd" . Uses 5 iterations of svdr from
the irlba package.
This is likely to give much faster but potentially less accurate results
than using "irlba" . For the purposes of nearest neighbor
calculation and coordinates initialization, any loss of accuracy doesn't
seem to matter much.
"bigstatsr" . Uses big_randomSVD
from the bigstatsr
package. The SVD methods used in bigstatsr may be faster on
systems without access to efficient linear algebra libraries (e.g.
Windows). Note: bigstatsr is not a dependency of
uwot: if you choose to use this package for PCA, you must install
it yourself.
"svd" . Uses svd for the SVD. This is
likely to be slow for all but the smallest datasets.
"auto" (the default). Uses "irlba" , unless more than
50
case "svd" is used.

binary_edge_weights 
If TRUE then edge weights in the input
graph are treated as binary (0/1) rather than real valued. This affects the
sampling frequency of neighbors and is the strategy used by the PaCMAP
method (Wang and coworkers, 2020). Practical (Böhm and coworkers, 2020)
and theoretical (Damrich and Hamprecht, 2021) work suggests this has little
effect on UMAP's performance.

nn_args 
A list containing additional arguments to pass to the nearest
neighbor method. For nn_method = "annoy" , you can specify
"n_trees" and "search_k" , and these will override the
n_trees and search_k parameters.
For nn_method = "hnsw" , you may specify the following arguments:

M The maximum number of neighbors to keep for each vertex.
Reasonable values are 2 to 100 . Higher values give better
recall at the cost of more memory. Default value is 16 .

ef_construction A positive integer specifying the size of
the dynamic list used during index construction. A higher value will
provide better results at the cost of a longer time to build the index.
Default is 200 .

ef A positive integer specifying the size of the dynamic
list used during search. This cannot be smaller than n_neighbors
and cannot be higher than the number of items in the index. Default is
10 .
For nn_method = "nndescent" , you may specify the following
arguments:

n_trees The number of trees to use in a random projection
forest to initialize the search. A larger number will give more accurate
results at the cost of a longer computation time. The default of
NULL means that the number is chosen based on the number of
observations in X .

max_candidates The number of potential neighbors to explore
per iteration. By default, this is set to n_neighbors or 60 ,
whichever is smaller. A larger number will give more accurate results at
the cost of a longer computation time.

n_iters The number of iterations to run the search. A larger
number will give more accurate results at the cost of a longer computation
time. By default, this will be chosen based on the number of observations
in X . You may also need to modify the convergence criterion
delta .

delta The minimum relative change in the neighbor graph
allowed before early stopping. Should be a value between 0 and 1. The
smaller the value, the smaller the amount of progress between iterations is
allowed. Default value of 0.001 means that at least 0.1
neighbor graph must be updated at each iteration.

init How to initialize the nearest neighbor descent. By
default this is set to "tree" and uses a random project forest.
If you set this to "rand" , then a random selection is used. Usually
this is less accurate than using RP trees, but for highdimensional cases,
there may be little difference in the quality of the initialization and
random initialization will be a lot faster. If you set this to
"rand" , then the n_trees parameter is ignored.

Details
lvish
differs from the official LargeVis implementation in the
following:
Only the nearestneighbor index search phase is multithreaded.
Matrix input data is not normalized.
The n_trees
parameter cannot be dynamically chosen based on
data set size.
Nearest neighbor results are not refined via the
neighborofmyneighbor method. The search_k
parameter is twice
as large than default to compensate.
Gradient values are clipped to 4.0
rather than 5.0
.
Negative edges are generated by uniform sampling of vertexes rather
than their degree ^ 0.75.
The default number of samples is much reduced. The default number of
epochs, n_epochs
, is set to 5000
, much larger than for
umap
, but may need to be increased further depending on your
dataset. Using init = "spectral"
can help.
Value
A matrix of optimized coordinates, or:
if ret_nn = TRUE
(or ret_extra
contains "nn"
),
returns the nearest neighbor data as a list called nn
. This
contains one list for each metric
calculated, itself containing a
matrix idx
with the integer ids of the neighbors; and a matrix
dist
with the distances. The nn
list (or a sublist) can be
used as input to the nn_method
parameter.
if ret_extra
contains "P"
, returns the high
dimensional probability matrix as a sparse matrix called P
, of
type dgCMatrixclass.
if ret_extra
contains "sigma"
, returns a vector of
the high dimensional gaussian bandwidths for each point, and
"dint"
a vector of estimates of the intrinsic dimensionality at
each point, based on the method given by Lee and coworkers (2015).
The returned list contains the combined data from any combination of
specifying ret_nn
and ret_extra
.
References
Belkin, M., & Niyogi, P. (2002).
Laplacian eigenmaps and spectral techniques for embedding and clustering.
In Advances in neural information processing systems
(pp. 585591).
http://papers.nips.cc/paper/1961laplacianeigenmapsandspectraltechniquesforembeddingandclustering.pdf
Böhm, J. N., Berens, P., & Kobak, D. (2020).
A unifying perspective on neighbor embeddings along the attractionrepulsion spectrum.
arXiv preprint arXiv:2007.08902.
https://arxiv.org/abs/2007.08902
Damrich, S., & Hamprecht, F. A. (2021).
On UMAP's true loss function.
Advances in Neural Information Processing Systems, 34.
https://proceedings.neurips.cc/paper/2021/hash/2de5d16682c3c35007e4e92982f1a2baAbstract.html
Dong, W., Moses, C., & Li, K. (2011, March).
Efficient knearest neighbor graph construction for generic similarity measures.
In Proceedings of the 20th international conference on World Wide Web
(pp. 577586).
ACM.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1145/1963405.1963487")}.
Kingma, D. P., & Ba, J. (2014).
Adam: A method for stochastic optimization.
arXiv preprint arXiv:1412.6980.
https://arxiv.org/abs/1412.6980
Lee, J. A., PeluffoOrdóñez, D. H., & Verleysen, M. (2015).
Multiscale similarities in stochastic neighbour embedding: Reducing
dimensionality while preserving both local and global structure.
Neurocomputing, 169, 246261.
Malkov, Y. A., & Yashunin, D. A. (2018).
Efficient and robust approximate nearest neighbor search using hierarchical
navigable small world graphs.
IEEE transactions on pattern analysis and machine intelligence, 42(4), 824836.
McInnes, L., Healy, J., & Melville, J. (2018).
UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction
arXiv preprint arXiv:1802.03426.
https://arxiv.org/abs/1802.03426
O’Neill, M. E. (2014).
PCG: A family of simple fast spaceefficient statistically good
algorithms for random number generation
(Report No. HMCCS20140905). Harvey Mudd College.
Tang, J., Liu, J., Zhang, M., & Mei, Q. (2016, April).
Visualizing largescale and highdimensional data.
In Proceedings of the 25th International Conference on World Wide Web
(pp. 287297).
International World Wide Web Conferences Steering Committee.
https://arxiv.org/abs/1602.00370
Van der Maaten, L., & Hinton, G. (2008).
Visualizing data using tSNE.
Journal of Machine Learning Research, 9 (25792605).
https://www.jmlr.org/papers/v9/vandermaaten08a.html
Wang, Y., Huang, H., Rudin, C., & Shaposhnik, Y. (2021).
Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering tSNE, UMAP, TriMap, and PaCMAP for Data Visualization.
Journal of Machine Learning Research, 22(201), 173.
https://www.jmlr.org/papers/v22/201061.html
Examples
# Default number of epochs is much larger than for UMAP, assumes random
# initialization. Use perplexity rather than n_neighbors to control the size
# of the local neighborhood 20 epochs may be too small for a random
# initialization
iris_lvish < lvish(iris,
perplexity = 50, learning_rate = 0.5,
init = "random", n_epochs = 20
)